Directional antenna having cosine shaped aperture



March 14, 1961 G. KOCH 2,975,420

DIRECTIONAL ANTENNA HAVING COSINE SHAPED APERTURE 2 Sheets-Sheet 1 Filed Oct. 4. 1955 F I G. I

8 0 5 [0 l5 20 INVENTOR:

GERHARD KOCH PATENT AGENT March 14, 1961 KOCH 2,975,420

DIRECTIONAL ANTENNA HAVING COSINE SHAPED APERTURE Filed 001;. 4. 1955 2 Sheets-Sheet 2 FIG. IO 1 FIG. |2 l5 INVENTOR GERHARD KOCH BY ZQM PATENT AGENT DIRECTIONAL ANTENNA HAVING COSINE SHAPED APERTURE Gerhard Koch, Ulm, Danube, Germany, assignor to Telefunken G.m.b.H., Berlin, Germany Filed (Pct. 4, 1955, Ser. No. 538,347

Claims priority, application Germany Oct. 4, 1954 8 Claims. (Cl. 343-786) The invention relates to directional antennas for very short electromagnetic waves using a so-called surface radiator. When such antennas are applied, for example, to directional radiation patterns, in radio links, in radar systems or the like, it frequently becomes desirable to select the side lobes in the transmitting plane very small, in order to avoid disturbing influences on other transmitting or receiving stations, or to avoid erroneous bearings. it has been known to design the aperture of the surface radiator with reference to the transmitting plane in the shape of a bell, whereby it is assumed that the density of the energizing rays of the surface radiator is homogeneous, i.e. the individual surface elements of the surface radiator thus receive the same electric excitation. In practice it is relatively difficult in many instances to obtain this homogeneous excitation density in a satisfactory manner, so that with such surface radiators the results obtained are inferior to those which are theoretically possible.

It is an object of the invention to make the laws for surface radiators of homogeneous excitation density applicable to surface radiators for non-homogeneous excitation density in modified form.

It is another object of the invention to select the boundary function of the surface radiator in accordance with its electrical density in such a manner that the boundary function of the aperture of the surface radiator represents a rhombic or bell-shaped function, in which x is the coordinate of the aperture plane, lying in the transmitting plane,

y is the coordinate of the aperture plane lying perpendicularly with respect to the transmitting plane,

f (x) is the boundary function of the aperture with the non-homogeneous density,

f (x) is the boundary function of the substituted aperture with homogeneous density.

d is the maximum dimension of the aperture perpendicular with respect to the transmitting plane.

The angle go is referred to for the purpose of describing the angular displacement of the side lobes in a horizontal plane with respect to the main lobe of the radiation pattern and will be referred to hereinafter as the angle of angular suppression in this plane.

Still further objects and the entire scope of applica:

fnite Sttes Patent bility of the present invention will become apparent from the detailed description given hereinafter; it should be understood, however, that that detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description.

In the drawings,

Figure l is a view in section into the apertures of two differently shaped surface radiators, the figure serving to illustrate a comparison between a rectangular aperture and one of more generalized shape;

Figure 2 is a schematic plan view of showing the placement of stations A, B, C and D in a directional transmitting system;

Figure 3 is an elevational view of a directional transmitting system employing a surface reflector to redirect the transmitted energy and send it to a receiver;

Figure 4 is a view in section looking into a rhombic radiator aperture, and a schematic representation of its characteristics;

Figure 5 is a view in section looking into an aperture of a radiator having an exponential boundary function;

Figures 6 and 7 are views in section looking into the apertures of two different radiators having cosine boundary functions;

Figure 8 is a schematic representation of the shape of an aperture of modified boundary function, the figure representing only the radiating surface Which is located above the transmitting plane;

Figure 9 is a graphical representation showing a comparison of the performance of the apertures according to the present invention with the performance of square and circular apertures;

Figure 10 is a cross section through a directional antenna designed in accordance with the present invention;

Figure 11 is a cross section through a horn-shaped parabolic antenna embodying the present invention in a form modified with respect to the structure of Figure 10;

Figure 12 is a front elevation showing the shape of the aperture of the antenna of Figure 11.

The invention will be explained as follows in detail with reference to examples. The theoretical relation between the most favorable boundary function, known per se, and the excitation density and favorable shape of the aperture in order to obtain the behavior of a surface refiector with a homogeneous density can be relatively easily understood, if the following assumptions are made.

The radiation pattern in the xz plane (i.e. (p=0) of a rectangular aperture with the sides 0, dr and the electric density distribution a(x) (see Figure 1) corresponds to the formula +C/2 jk 2 sin 0 X,(17)=d,-fa(x) -e A in 2 while the radiation pattern in the x-z plane of an aperture with homogeneous density with any boundary function f(x) and with the same dimensions in the x-axis corresponds to the formula In this formula d is the largest dimension of the aperttn'e of any size in the y-axis.

The Equations 2 and 3 are equal when f(x) =a(x), i.e. the radiation pattern of the rectangular aperture with the density a(x), is equal to the radiation pattern of an aperture with homogeneous density with a boundary function f(x)=a(x), having the same dimension in the x-axis. The same is true for the radiation pattern in the y-z plane, if the boundary function f(y) equals the density function w(y) and the dimension d is selected equal in both cases. a

In other Words, an aperture with homogeneous density and of any configuration in a certain plane results in the same radiation pattern as a rectangular aperture of the same extension in this plane having a corresponding density, see Figure 1.

This analogy between density and configuration of the aperture can be extended in such a manner that an aperture of any dimension and any density can be transposed to its diagram in a certain plane (for example horizontal diagram) to an apeiture with homogeneous density of a certain predetermined configuration. This configuration is obtained from the density and the configuration of the aperture of non-homogeneous density. The following mathematical term is obtained for the radiation characteristic of an aperture with non-homogeneous density having the boundary function f,-(x) and the density function a(x, y):

The radiation pattern in the transmitting plane will be, if 50:0:

By a comparison with the corresponding formula for the homogeneous density (see Equation 3) +c/2 j -z-sin t) X.o 'ff. x -e A w 3) it can be recognized that the horizontal pattern of the aperture with non-homogeneous density equals the aperture with homogeneous density, if

Thus, in case of non-homogeneous density principally the same angular suppressions are obtained for the horizontal pattern as in case of homogeneous density. The knowledge and laws obtained in the case of the aperture with homogeneous density can be applied to the aperture with non-homogeneous excitation density to ascertain the dimensions in View of the large angular suppression, i.e. the configuration of the aperture with non-homogeneous density is selected in such manner that there is obtained for the substituted homogeneous density aperture, according to Equation 6, one of the shapes found suitable for homogeneous density with an angular suppression as small as possible. The boundary function f (x) of the substituted aperture with homogeneous density is given a curve which at least approximates the shape of a bell, i.e. particularly the curve of the function cos x or of a binominal function or of other functions for homogeneous density which will be explained in the following.

If a(x, y):a(x), i.e. if the density function depends only on x, the Equation 6 becomes:

In other words, the configuration of the homogeneous substituted aperture has to be simply a product of the density times the configuration of the non-homogeneous aperture. Thus, for example, with a density distribution according to COS and a boundary of the function tr-d; COS 6 referred to the transmitting plane, the same radiation pattern is obtained in the transmitting plane as in the aperture with homogeneous density. I

Consequently, by suitable configuration of the aperture of a surface reflector in dependence on the density, and vice versa, the angular suppression of surface reflectors in the transmitting plane can be considerably improved.

The shapes mentioned in the introduction include particularly suitable forms for the aperture with homogeneous density and will be explained in the following for the better understanding of the invention.

The requirements to be fulfilled by the radiation diagram of a directional antenna are different, depending upon the particular application. Mostly small side lobes of the radiation diagram are required. In case of antennas of the directional transmission systems, this requirement for small side lobes is due to the desire to use very few high-frequency channels. A transmitter operating on a certain frequency can disturb a receiver operating on the same frequency which actually should receive only energy from another transmitter. The required difference between useful signal and interference or disturbing signal can amount up to 80 db, depending upon the kind of system. Therefore, the requirements for eliminating the side lobes of the directional antenna are extremely high under certain circumstances. These requirements are not fulfilled by the antenna heretofore used, so that the desired freedom from cross-talk at the selected frequency is not obtained. Figure 2 of the drawings shows the stations A, B, C and D of a directional transmitting system, the fields of which are alternately operated at the frequencies I and II. In case of a straight system, the antenna of the station A would radiate directly with its main lobe to the antenna of the station D. Therefore, a zigzag line is provided, so that the transmitter antenna of the station A radiates with a field strength to D, which strength is lower with respect to the main lobe, whereby the decrease is determined by the directional diagram and the angle 5 In the same way, the receiving antenna at D receives at a strength which is lower with respect to the main lobe.

Consequently, the suppression of radiated energy given by the-pattern and the angle'S is to be made as large -as possible. In other words, the side lobes of the antennas are to be made as small as possible.

When considering a radiation pattern generally, only the size of the side lobes is discussed. However, not only the size of the side lobes is of importance, but also their angular displacement from the main lobe and, in case of a wide main lobe, also the shape of the latter. Therefore, the term angular suppression is used to designate a measure of the decrease in the side-lobe radiation energy (measured in db relative to the main lobe), if one deviates by a certain angle 3 from the main direction of radiation. In practice, Within the range of the side lobes, the envelope of the radiation pattern for the angular suppression is critical.

In the directional transmission technique mostly very highly focused antennas are required. This is the reason that almost all surface radiators, such as parabolic mirrors, lens antennas, horn-shaped radiators or plane mirrors, are employed for focusing or reflecting purposes. Included in these kinds of antennas should also be dipole-arrays having a great number of discrete radiators and/or reflectors, such as used for example in the ultra short wave directional transmission technique.

It has been known in connection with surface radiators to increase the angular suppression by providing a density of the electric excitation decreasing towards the edge, as inherently occurs in parabolic mirrors, lens antennas and horn radiators to a larger or smaller extent.

However, the increase of the angular suppression is practically limited in this way, because with a density decreasing towards the edge there results a considerable decrease in the efliciency of the surface-area utilization, i.e. of the antenna gain, as compared with the case of homogeneous density. This decrease in efliciency is the bigger, the more the density decreases towards the edge, i.e. the smaller the side lobes are intended to be. Furthermore, it is diflicult to realize a suitable density pat tern for very big angular suppressions. Finally, there are instances in which an approximately homogeneous density is present. If, for example, as shown in Figure 3, one station A of a directional transmission system is in a valley and is not within View of the opposite station 13, a transmission link is only possible via an intermediate station A said intermediate station being designed as a plane reflecting mirror, whereby it is assumed that the distance between A and A is not too great. Such a reflecting mirror acting as a relay is excited by an approximately plane wave-front, because the distance amounts generally to from one hundred to some thousand meters. Therefore, it is practically impossible to illuminate this mirror other than homogeneously.

This case of a reflecting mirror acting as a relay has to be distinguished from a reflecting mirror mounted on the top of a mast, said latter mirror being acted upon by rays transmitted to it from the foot of the mast. Such reflecting mirror, due to its distance from the active antenna of only 20 to 80 meters, is almost always nonhomogeneously illuminated. Therefore, it is advantageous to consider this reflecting mirror together with the reflector on the ground as an antenna unit of a certain radiation pattern and gain. Obviously, the teachings according to the invention can be applied to such reflecting mirrors to obtain small side lobes, though not under the assumption of a homogeneous density.

It has been known to calculate the radiation of a surface radiator, if its dimensions are large, with reference to the wave-length, with good approximation by using the Huyghens principle in the scalar form of Kirchhoff, as the radiation pattern of a corresponding opening with corresponding electrical excitation in an infinitely extended plane reflecting surface as a substitute. This opening represents the aperture. In this case it is advantageous to confine these considerations to the remotely located field, because the stations may be affected by an interference by undesirable radiations and, therefore, in all practical cases have been located at such distance that the local field was excluded. For example, for an antenna surface of 1600A (very large surface radiator) at a distance of about 3200A, practically only the remote field component has to be taken into account.

The possibilities of a further decrease of the influence of the side lobes will be explained in the following with reference to Figure 4. These considerations are based upon the experience that the larger a reflector, the sharper it focuses. Theoretical or numerical analysis has shown that these considerations can also be applied to a surface radiator. For this purpose the surface radiator, according to the embodiment of Figure 4, is designed in rhombic form, i.e. the diagonal length in the vertical plane 0! is selected smaller than the horizontal length 0 in the transmitting planes. The pattern of such surface radiator for homogeneous density is obtained by the equation sin f -sin 19(cos h -sin 0)] -sin i9 cos h z-sin (p) sin a sin a The three-dimensional coordinate system which is the basis of the formula is for the sake of completeness shown in Figure 4.

it can be seen from the general form of the Equation 8 that the side lobes, as compared to the main lobe of the radiation, remained unchanged with respect to the square mirror, i.e. that the radiation pattern in the plane of the pattern determined by the diagonal c for o=0 does not depend upon d, i.e. is independent of the shape of the rhomb. Furthermore, in analogy to the radiation pattern of the rectangular surface, the radiation pattern in the c plane is independent from c with respect to the size of the side lobes. Thus, only the angular distribution of the side -lobes is determined by the value c, i.e. the radiation pattern is narrowed with increasing 0. This increased concentration means a more rapid decrease in the side lobe radiation in the transmission plane, if the radiation is considered in the transmitting plane from the main lobe toward a side lobe. These considerations apply to any form of a surface radiator with homogeneous density as shown in the embodiments of this invention, symmetrically with respect to the transmitting plane. It is possible, however, to consider for example only that half of the surface radiation which lies above the transmitting plane.

The side lobe suppression in the transmitting plane can be further increased by selecting the effective shape of the surface radiator in such a manner that the side lobes in the transmitting plane are still more suppressed than is the case in the diagonal plane of a square or rhombic shaped surface radiator. This is derived from the analog of the Equations 2 and 3, according to which certain relations between the boundary function of an aperture and the excitation density are given, as has been explained in the foregoing with reference to Figure 4.

Disregarding for the moment the difficulties in practical application, based on this analog it appears to be theoretically possible to select a boundary in accordance with a binominal distribution, i.e. according to the function which theoretically causes the side lobes to disappear completely, because a rectangular surface with such density does not radiate side lobes. Thus 6 represents a constant which can be freely selected.

With such a boundary function the side lobes of the surface radiator in the transmitting plane are very small compared with a square mirror, even if the boundary function, as shown in Figure 5,,is cut otf at a finite value of y=f(x) with The function would require that the surface radiator have the vertical dimension y= at infinity.

In comparing the angular suppression of the horizontal patterns of different aperture forms, a suitable basis for comparison has to be agreed upon. A basis for comparison of the same surface area but of the different shapes is chosen, whereby the ratio c/d is assumed for the sake of simplicity to be 1 in the following analysis. This assumption does not affect the following considerations with respect to their general application or validity in the following analysis, because the value d does not appear in the pattern of the horizontal plane, or the transmitting plane (x-z plane), and in the patterns of the neighboring planes to a small extent, particularly as long as d does not greatly deviate from c, which is true in most practical cases.

In practice it is generally unimportant to decrease the side lobes by employing additional mechanical means. It is, however, important to obtain an angular suppression as large as possible with a particular aperture form of given surface dimensions. Furthermore, it is an important consideration in the design of a directional antenna to determine how large its maximum extensions or dimensions are in comparison with a square having the same surface area, or how large its surface is in comparison to a square which it just frames. This degree of coverage of the frame square will be denoted in the following analysis by 1 In the case of surfaces which have not the same maximum dimensions in each direction, a framing rectangle should be used as the basis.

In the case of a rhombic surface radiator, i.e. for 0 d, in which case a square which is contacted on its corners, 1 ='0.5. This value 0.5 will be used in the following as a practical lower limit of the value, in order to provide a basis for comparison among the various surface radiator shapes. In practice, this a value does not represent a rigid limit because it is critical, since in some cases the shape of the required radiation pattern may permit the use of a lower 1 value.

In further consideration, a value of n =O.5 requires that in case of an exponential boundary curve having the special shape of a binominal distribution, cut-off takes place at a y value of 0.0451. Smaller y values are not significant, because of the presumption that the y dimension should be substantially larger than the wavelength and this presumption is no longer fulfilled. Thus, under this circumstance the desired radiation pattern will be disturbed. This disadvantage can be eliminated by polarizing the energizing signal in such a manner that the currents in the aperture flow only in the x direction, whereby the transverse dimension in the y direction becomes less critical where the transverse dimension is substantially below the wavelength.

Considerably better results with respect to angular suppression and the bulkiness of the antenna can be obtained, if a boundary function is applied which is described by the function y=f(x) =cos x, and particularly with a value of n in which the function equals Zero at a finite value of x at a horizontal tangent, whereby x is the horizontal. In this case It means a positive real constant which can be selected in accordance with the desired pattern requirements.

It was proven suitable to select the value It as 1, 2 or 3, whereby for n=1 the shape of the curve is shown in Figure 6 and for n=2 the shape of the curve in Figure 7.

The boundary function cos (x) for 11:2, in which case a will not be lower than 0.5, results in c=d= 28.3)\, i.e. a surface of 400W, with a radiation pattern, the first side lobe of which lies in the transmitting plane then at 31.3 db, the second side lobe then at 41.7 db, and the third side lobe then at 48.9 db below the main lobe. These side lobe values are considerably lower than those obtainable, for example, with a square radiator with homogeneous density.

The radiation pattern of. a surface radiator having the cos boundary in the horizontal or transmitting plane -sin 17 corresponding to the division of the boundary function y=f(x) =cos )=0.5+0.5 cos 12 This analog can be further exploited.

If the values of the individual components of a radiation pattern, for example those in Equation 11, are exactly of opposite phases in their side lobes, the angular suppression at a certain chosen radiation angle or angular range can be theoretically made infinite by equalizing the absolute values of the two components at this radiation angle. This is accomplished by selecting a boundary function in which, in place of the two 0.5 values in Equation 12, two other values, different from one another and fulfilling the mentioned conditions, are inserted. In this case it must be taken into consideration that, with other radiation angles, the angular suppression will be correspondingly decreased. In practice, such radiation pattern is always suitable, if the influence of the side radiation at a certain radiation angle can be made negligibly small.

The application of a boundary function corresponding to a higher-order cosine function theoretically results in a further increase of the angular suppression. If, however, the agreed analogy to a square is used, the degree of coverage 1 of the frame square is simultaneously decreased. Thus, for example, with a limit function whereby k is a constant 'to be freely selected between zero and a value smaller than one. In case of k=1, the value of the function corresponds to a rectangle, while for k=0 2. bell-shaped curve is obtained without discontinuitiesy For values of k between zero and one a boundary function is obtained which approximately corresponds to that of the curve of the function illustrated by a dotted line, i.e. a bell-shaped curve of a greater or lesser curvature having discontinuities at thevalues The results obtainable with the surface radiator forms, described in the examples, are plotted in the diagram of Figure 9 in comparison with square and circular surface radiators. In this diagram the radiation angles are referred to the main lobe, while the corresponding angular suppressions in db referred to the main lobe are plotted on the ordinate and in the range of the side lobes the encompassing curves. The reference numerals indicated by primes relate to the side radiation, while the reference numerals without primes designate the main radiation. The curves designated by 1, 1 correspond to a square surface radiator, one of the side edges of which'runs parallel to the transmitting plane, whereby c =20h and n =1. The curves 2, 2 correspond to a conventional circular surface radiator, whereby c=l.l27c and n =0.785, While curve 3 represents the course of the radiation patterns of a surface radiator with a binominal boundary function in which c:\/ 2 .c and a -=05. The curves 4, 4' represent the radiation pattern of a rhombic surface radiator with c=\/.c and n =0.5, while the curves 5, 5 and 6, 6' represent the radiation pattern of a surface radiator with cosine or cosine boundary function, whereby the cosine radiator has a c==l.25.c and =0.64, while the cosine surface radiator has a c== /2c and =0.5. This shows that the binominal function configuration or the rhombic shape as well as the cosine function configuration result in substantially more favorable values for angular suppression than the shapes of the surface radiators heretofore known, i.e. the square and circular surface radiators. It has been proven in practice that the corners can be suitably eliminated in view of a simpler construction and to avoid a bulky design. Such elimination has generally no influence on the angular suppression.

The problem, the solution of which is the object of the present invention, occurs particularly in so-called conical or cylindrical horn radiators in which the excitation density of the aperture is, to a certain extent, a lametion of the shape of the aperture. As it has been proven in practice that the values of the side lobes theoretically ascertained for a surface radiator, in accordance with the foregoing formulas, cannot be obtained when the surface radiator is designed as a parabolic mirror with an exciting antenna, it is recommended to provide as a radiating surface a cut-out portion of a cylindrical or rotatable paraboloid, which cut-out portion is arranged eccentrically with respect to the axis of rotation or plane of symmetry of the paraboloid.

This additional point of the invention is based upon the discovery that the above described behavior is a result of the disturbing influence of the exciting antenna lying in the field of the Wave reflected by the parabolic mirror. These reflected waves cause additional side lobes at the exciting antenna, said lobes partially exceeding the sidelobe values theoretically found for the surface radiator itself. It has been known to use in a normal parabolic mirror antenna an eccentric cut-out portion of a cylindrical paraboloid as radiating surface. However, in these known surface radiators the essential feature of the invention, namely, the construction according to the inventive teachings, is lacking.

Figure is a cross-section through a directional antenna designed in accordance with the invention. An energizing antenna 12 is located at focus 8 of the sector 11 eccentrically arranged with respect to the axis of rotation 9 of a rotatable paraboloid 10 in such manner, that the sector is illuminated by the rays in accordance with the formula given in the foregoing. For example, this formula may involve the maximum utilization of the surface obtained in a manner known per se. Any other conventional kinds of excitation used for parabolic mirror antennas of this type may be applied.

The present invention can also be applied to so-called horn-shaped parabolic structures, such as shown in Figures Ill and 12. These kinds of antennas have been known per se and are described in issues of the Bell System Technical Journal of recent years. Figure 11 shows a crosssection, and Figure 12 shows a front view of this kind of antenna in which the aperture 14 is formed according to a cosine function in accordance with the invention. The shape of the aperture 14, the front view of which is illustrated in Figure 12, corresponds approximately to the shape of the parabolic sector 11 of Figure 10. These so-called horn-shaped parabolic antennas are distinguished from the conventional parabolic mirror antennas primarily in that an exciting radiator proper, serving as feeding means, is lacking and a conventional tubular conduit 15 is gradually and continuously expanded, whereby an eccentric parabolic sector 16 is energized by the wave. The parabolic sector 16 may be in the form of a cylindrical parabolic construction or in the form of a paraboloid of rotation.

The eccentricity and the size of the parabolic sector 11 in the embodiment of Figure 10 is suitably selected in accordance with the structural and electrical requirements. The eccentricity is preferably selected in such manner that the exciting antenna is arranged as far as possible from the lower mirror edge in the direction of the aperture plane with the result that the mirror back reflection is simultanously progressively decreased. The opposite requirement is the result of the desire to avoid bulkiness in the antenna construction as far as possible, so that a compromise value must be selected which fulfills in practice the opposing requirements in a satisfactory manner. The term mirror back reflection means the radiation reflected back from the mirror to the exciting antenna.

Although, in accordnace with the provisions of the patent statutes, this invention is described as embodied in a concrete form and the principle of the invention has been explained together with the best mode in which it is now contemplated to apply that principle, it will be understood that the elements, combinations shown and described, are merely illustrative and that the invention is not limited thereto, since alterations and modifications Will readily suggest themselves to persons skilled in the art without departing from the true spirit of the invention or from the scope of the annexed claims.

I claim:

1. In a directional antenna system for radiating very short electro-magnetic Waves, a. surface radiator having x and y coordinates defining the shape of its radiating surface as viewed from the z direction of propagation, said radiator propagating said waves in a lobe which is focussed in the xz plane, said radiator comprising a plurality of surface elements all lying parallel to the xz plane and disposed symmetrically on each side of the y axis, the boundary function of the radiating surface as viewed from the z-direction and defined by the ends of all of said surface elements being y= i i-fit and being selected in dependence on the excitation density of the radiator a(x, y) in such a manner that wherein f (x) is a cosine boundary function of the aperture having non-homogeneous excitation density;

f (x) is the boundary function of an aperture having homogeneous excitation density and having the same radiation pattern in the x-z plane, and

d is the maximum aperture dimension in the y-direction.

2. In a directional antenna system according to claim 1, the curve of the boundary function being bell-shaped and symmetrical on each side of the x-axis.

3. A directional antenna system according to claim 1, wherein the radiator is designed in such manner that the contour of its radiating surface as viewed from the z-direction is substantially symmetrical with respect to the xz plane.

11 4. A directional antenna system, according to claim 2, wherein the curve of the function is' selected substantially according to the function y=cos x, in which n is any exponent, the value of which is larger than zero.

5. A directional antenna system, according to claim 2, wherein the curve of the function is selected in such a way that the characteristic function of the said radiating surface in the x-z plane consists of two out-of-phase components with angle-dependent values, and wherein, for the purpose of obtaining a high degree of freedom from side radiation over a particular radiation angular range, the said radiating surface is further designed in such manner that said components of the characteristic function have the same values at the given radiation angular range.

6. A directional antenna system, according to claim 5, wherein the curve of the function is selected according to the equation car- 7. A directional antenna system, according to claim 6, wherein a surface radiator is provided comprising a sector surface substantially in the form of a paraboloid in which of rotation having an excitation antenna at its focus, and wherein said radiating surface as viewed from the zdirection is provided opposite the radiating sector surface, said sector lying eccentrically with respect to the axis of 5 rotation of the paraboloid.

8. A directional antenna system, according to claim 6, wherein a surface radiator is provided comprising a sector surface substantially in the form of a para-boloid having an excitation antenna at its focus line, and where- 10 in said radiating surface as viewed from the z-direction is provided opposite the radiating sector surface, said sector lying eccentrically with respect to the plane of symmetry.

15 References Cited in thefile of this patent OTHER REFERENCES Microwave Antenna, McGraw-Hill, by S. Silver, 1949, Theory and Design (Table 6-1, page 87).

The International Dictionary of Physics and Elec- 30 tronics, Van Nostrand Co. (1956). 

